Expression of type ExprTuple

from the theory of proveit.linear_algebra.vector_sets

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, K, Lambda, V, n
from proveit.core_expr_types import a_1_to_n, x_1_to_n
from proveit.linear_algebra import LinDepSets, VecSpaces, VecZero, lin_comb_axn, some_nonzero_a
from proveit.logic import Equals, Exists, Forall, InSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(InSet(Set(x_1_to_n), LinDepSets(V)), Exists(instance_param_or_params = [a_1_to_n], instance_expr = Equals(lin_comb_axn, VecZero(V)), domain = K, condition = some_nonzero_a).with_wrapping()).with_wrapping_at(2), domain = V).with_wrapping(), domain = NaturalPos), domain = VecSpaces(K))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{n \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{LinDepSets}\left(V\right)\right) =  \\ \left[\begin{array}{l}\exists_{a_{1}, a_{2}, \ldots, a_{n} \in K~|~\left(a_{1} \neq 0\right) \lor  \left(a_{2} \neq 0\right) \lor  \ldots \lor  \left(a_{n} \neq 0\right)}~\\
\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) = \vec{0}\left(V\right)\right)\end{array}\right] \end{array} \end{array}\right)\end{array}\right]\right]\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 78 body: 2
2	Operation	operator: 19 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 68 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 19 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	68, 12
11	Lambda	parameter: 76 body: 14
12	Operation	operator: 15 operand: 78
13	ExprTuple	76
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	78
17	Operation	operator: 19 operand: 22
18	Operation	operator: 72 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	76, 23
22	Lambda	parameters: 41 body: 24
23	Literal
24	Conditional	value: 25 condition: 26
25	Operation	operator: 52 operands: 27
26	Operation	operator: 54 operands: 28
27	ExprTuple	29, 30
28	ExprTuple	31
29	Operation	operator: 72 operands: 32
30	Operation	operator: 33 operand: 38
31	ExprRange	lambda_map: 35 start_index: 75 end_index: 76
32	ExprTuple	36, 37
33	Literal
34	ExprTuple	38
35	Lambda	parameter: 90 body: 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operand: 68
38	Lambda	parameters: 43 body: 44
39	Operation	operator: 72 operands: 45
40	Literal
41	ExprTuple	46
42	Literal
43	ExprTuple	47
44	Conditional	value: 48 condition: 49
45	ExprTuple	84, 68
46	ExprRange	lambda_map: 50 start_index: 75 end_index: 76
47	ExprRange	lambda_map: 51 start_index: 75 end_index: 76
48	Operation	operator: 52 operands: 53
49	Operation	operator: 54 operands: 55
50	Lambda	parameter: 90 body: 84
51	Lambda	parameter: 90 body: 85
52	Literal
53	ExprTuple	56, 57
54	Literal
55	ExprTuple	58, 59
56	Operation	operator: 60 operands: 61
57	Operation	operator: 62 operand: 68
58	ExprRange	lambda_map: 64 start_index: 75 end_index: 76
59	Operation	operator: 65 operands: 66
60	Literal
61	ExprTuple	67
62	Literal
63	ExprTuple	68
64	Lambda	parameter: 90 body: 69
65	Literal
66	ExprTuple	70
67	ExprRange	lambda_map: 71 start_index: 75 end_index: 76
68	Variable
69	Operation	operator: 72 operands: 73
70	ExprRange	lambda_map: 74 start_index: 75 end_index: 76
71	Lambda	parameter: 90 body: 77
72	Literal
73	ExprTuple	85, 78
74	Lambda	parameter: 90 body: 79
75	Literal
76	Variable
77	Operation	operator: 80 operands: 81
78	Variable
79	Operation	operator: 82 operands: 83
80	Literal
81	ExprTuple	85, 84
82	Literal
83	ExprTuple	85, 86
84	IndexedVar	variable: 87 index: 90
85	IndexedVar	variable: 88 index: 90
86	Literal
87	Variable
88	Variable
89	ExprTuple	90
90	Variable